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The game theoretic study of coalitions focuses on settings in which commitment technologies are available to allow groups to coordinate their actions. Analyses of such settings focus on two questions. First, what are the implications of the ability to make commitments and form coalitions for how games are played? Second given that coalitions can form, which coalitions should we expect to see forming? I examine classic cooperative and new noncooperative game theoretic approaches to answering these questions. Classic approaches have focused especially on the first question and have produced powerful results. However, these approaches suffer from a number of weaknesses. New work attempts to address these shortcomings by modeling coalition formation as an explicitly noncooperative process. This new research reintroduces the problem of coalitional instability characteristic of cooperative approaches, but in a dynamic setting. Although in some settings, classic solutions are recovered, in others this new work shows that outcomes are highly sensitive not only to bargaining protocols, but also to the forms of commitment that can be externally enforced. This point of variation is largely ignored in empirical research on coalition formation. I close by describing new agendas in coalitional analysis that are being opened up by this new approach. Adapted from the source document.

While widely applied to political coalitions in national assemblies and cabinets, theories of coalition formation have seldom been tested at the local level of government. This article presents a model of coalition formation in connection with mayoral elections in Norwegian local councils and tests it on the basis of the first systematic collection of data on the election of mayors from a large number of municipalities. It finds small significant effects on the probability that oversized coalitions will be formed. Contrary to "common" knowledge, the size of a municipality has a positive influence on the conflictual climate, and thus on the size of the coalitions formed, which implies that the probability that an oversized coalition will form is higher in a large than in a small municipality. It also finds that the possibility that an oversized coalition will form increases if one party controls a majority of the councilors on its own, and if the majority is non‐socialistically controlled. The assumption of a strong norm for reaching consensus‐based decisions, reinforced by the design of the local political institutions, is supported.

The necessity of forming coalitions is inevitable in a large, diverse nation in which political power is fragmented both vertically & horizontally. Presidents invest substantial time & effort building supporting coalitions for themselves & their polices among the public & within Congress. The author explores the president's ability to build coalitions, examines the relationship between the institutional presidency & obstacles to coalition building, & inquires whether the presidency as an institution is adequate to the task of building the coalitions necessary for governing. He concludes that (1) the president has great difficulty building coalitions for governing among the public & within Congress; (2) the institutional structure of the presidency (& Congress) is at the core of the difficulty of building coalitions in Congress but does not inhibit obtaining public support; & (3) the changes required to notably improve presidential coalition building are so fundamental that they are unlikely to occur. 3 Tables, 128 References. Adapted from the source document.

This chapter surveys the sizable and growing literature on coalition formation. We refer to theories in which one or more groups of agents ("coalitions") deliberately get together to jointly determine their actions. The defining idea of a coalition, in this chapter, is that of a group which can coordinate agreements among its members, while it interacts noncooperatively with other non-member individuals and the outside world in general. It is hard to overstate the importance of coalition formation in economic, political and social analysis. Ray (2007) gives several examples in which such a framework comes to life: cartel formation, lobbies, customs unions, conflict, public goods provision, political party formation, and so on. Yet as one surveys the landscape of this area of research, the first feature that attracts attention is the fragmented nature of the literature. The theories that bear on our questions range from collusive behavior in repeated games, to models of bargaining, to cooperative game-theoretic notions of the core, or notions of coalition-proofness in noncooperative games. To unravel the many intricacies of this literature would take far more than a survey. To prevent our terms of inquiry from becoming unmanageably large, we impose a basic restriction.

This paper examines recent theoretical developments of the theory of coalition stability. It focuses on the relationship between the incentives to defect from a coalition, the size of the resulting equilibrium coalition structure, and the different assumptions on membership rules, coalition behaviour, players' conjectures, etc. The paper considers several cases. Simultaneous vs. sequential moves, linear vs. circular order of moves, Nash vs. rational conjectures, open vs. exclusive membership, monotonic vs. non monotonic payoff functions, and orthogonal vs. non-orthogonal reaction functions. The profitable and stable coalition will be derived for each possible configuration of the rules of the game, the payoff functions and the membership rules. The results show that the size of the profitable and stable coalition highly depends on the chosen configuration and that the equilibrium outcome ranges from a small coalition with a few signatories to full cooperation. The paper explores under which conditions a large stable coalition is likely to emerge, and identifies the institutional setting that favours the emergence of such coalition.

The author compares the trajectories of three U.S. policies from 1935 to 1952: the Agricultural Adjustment Act (AAA), the National Labor Relations Act (NLRA), and the Social Security Act (SSA). Agricultural policy expanded beyond the New Deal, labor policy was severely weakened, and social security saw only minor changes. Why? Class coalitions strongly influenced the trajectories of these policies. The coalition supporting the AAA largely maintained, but the coalition supporting the NLRA collapsed. Support from southern planters was particularly important for each policy. Focusing on trajectories rather than merely policy formation more clearly demonstrates the influence of class coalitions over state policy.

AbstractFrom 1987 to 1998, the Basque government was made up of a coalition between Basque nationalists and unionists. However, there are doubts about whether this experience has a consociational character. In order to clarify this, the article analyses the four characteristics of Lijphart's scheme, focussing on the degree of power‐sharing of the Basque governments using the qualitative distinction of McGarry and O'Leary and the centripetal approach, creating the power‐sharing in government index and studying the degree of ideological proximity of the parties making up the coalition. The conclusions are that in the Basque case, there were no complete or concurrent consociational governments, but instead, there were centripetal coalitions. Furthermore, it makes clear that an electoral system with high proportionality is an obstacle when it comes to maintaining cross‐segment governments in societies that lack stability in the correlation of forces among segments and use centripetal power‐sharing coalitions or weak or concurrent consotiational coalitions. The most realistic choice in order to preserve the power‐sharing government would be adopting a proportional sequential coalition and a proportional electoral system with significative electoral threshold to avoid the emergence of anti‐consociational parties.

The Shapley value for an n-person game is decomposed into a 2n × 2n value matrix giving the value of every coalition to every other coalition. The cell ϕIJ(v, N) in the symmetric matrix is positive, zero, or negative, dependent on whether row coalition I is beneficial, neutral, or unbeneficial to column coalition J. This enables viewing the values of coalitions from multiple perspectives. The n × 1 Shapley vector, replicated in the bottom row and right column of the 2n × 2n matrix, follows from summing the elements in all columns or all rows in the n × n player value matrix replicated in the upper left part of the 2n × 2n matrix. A proposition is developed, illustrated with an example, revealing desirable matrix properties, and applicable for weighted Shapley values. For example, the Shapley value of a coalition to another coalition equals the sum of the Shapley values of each player in the first coalition to each player in the second coalition. ; publishedVersion

Formal coalition theory has tended to ignore the existence of local government coalitions. Local government studies have tended to ignore the existence of formal coalition theory. Yet local administrations frequently comprise coalitions of parties. There is clearly a need, therefore, to bring the two areas of study together.

"Coalition signals can offer crucial information to voters during political campaigns. In
multiparty systems, they reduce the number of theoretically possible coalitions to a
much smaller set of plausible and likely coalitions. Strategic voters who care more
about the formation of the next coalition government than supporting the preferred
party might, for example, defect from the preferred party in favor of another party that
might produce a more desirable coalition government. For other voters, coalition
signals might merely elicit affective responses which can shift the vote. In this study,
we investigate whether and how different coalition signals affect vote intentions and
activate different party and coalition preferences. We report the results of a nationally
representative survey experiment conducted before the 2006 Austrian General
Election. Respondents encountered four vignettes with hypothetical coalitions, each
followed by the standard vote intention question. The results indicate that voters are
responsive to coalition signals, and especially voters with two preferred parties tend to
change their vote intentions. Finally, a more detailed look at Green Party voters
suggests that individual party and coalition preferences help to explain the direction of
these changes." (authors abstract)